Clausius–Mossotti relation

In electromagnetism, the Clausius–Mossotti relation, named for O. F. Mossotti and Rudolf Clausius, expresses the dielectric constant (relative permittivity, $ε r$ ) of a material in terms of the atomic polarizability, $α$ , of the material's constituent atoms and/or molecules, or a homogeneous mixture thereof. It is equivalent to the Lorentz–Lorenz equation, which relates the refractive index (rather than the dielectric constant) of a substance to its polarizability. It may be expressed as:

{\frac {\varepsilon _{\mathrm {r} }-1}{\varepsilon _{\mathrm {r} }+2}}={\frac {N\alpha }{3\varepsilon _{0}}}

where

$\varepsilon _{r}={\tfrac {\varepsilon }{\varepsilon _{0}}}$ is the dielectric constant of the material, which for non-magnetic materials is equal to $n 2$ , where $n$ is the refractive index;
$ε 0$ is the permittivity of free space;
$N$ is the number density of the molecules (number per cubic meter);
$α$ is the molecular polarizability in SI-units [C·m²/V].

In the case that the material consists of a mixture of two or more species, the right hand side of the above equation would consist of the sum of the molecular polarizability contribution from each species, indexed by $i$ in the following form:

{\frac {\varepsilon _{\mathrm {r} }-1}{\varepsilon _{\mathrm {r} }+2}}=\sum _{i}{\frac {N_{i}\alpha _{i}}{3\varepsilon _{0}}}

In the CGS system of units the Clausius–Mossotti relation is typically rewritten to show the molecular polarizability volume $\alpha '={\tfrac {\alpha }{4\pi \varepsilon _{0}}}$ which has units of volume [m³]. Confusion may arise from the practice of using the shorter name "molecular polarizability" for both $\alpha$ and $\alpha '$ within literature intended for the respective unit system.

The Clausius–Mossotti relation assumes only an induced dipole relevant to its polarizability and is thus inapplicable for substances with a significant permanent dipole. It is applicable to gases such as N₂, CO₂, CH₄ and H₂ at sufficiently low densities and pressures. For example, the Clausius–Mossotti relation is accurate for N₂ gas up to 1000 atm between 25 °C and 125 °C. Moreover, the Clausius–Mossotti relation may be applicable to substances if the applied electric field is at a sufficiently high frequencies such that any permanent dipole modes are inactive.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.